More pubkey doc updates

1 files changed, 154 insertions, 0 deletions

diff --git a/doc/examples/factor.cpp b/doc/examples/factor.cpp
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+/*
+* (C) 2009-2010 Jack Lloyd
+*
+* Distributed under the terms of the Botan license
+*
+* Factor integers using a combination of trial division by small
+* primes, and Pollard's Rho algorithm
+*/
+
+#include <botan/botan.h>
+#include <botan/reducer.h>
+#include <botan/numthry.h>
+using namespace Botan;
+
+#include <algorithm>
+#include <iostream>
+#include <iterator>
+
+namespace {
+
+/*
+* Pollard's Rho algorithm, as described in the MIT algorithms book. We
+* use (x^2+x) mod n instead of (x*2-1) mod n as the random function,
+* it _seems_ to lead to faster factorization for the values I tried.
+*/
+BigInt rho(const BigInt& n, RandomNumberGenerator& rng)
+   {
+   BigInt x = BigInt::random_integer(rng, 0, n-1);
+   BigInt y = x;
+   BigInt d = 0;
+
+   Modular_Reducer mod_n(n);
+
+   u32bit i = 1, k = 2;
+   while(true)
+      {
+      i++;
+
+      if(i == 0) // overflow, bail out
+         break;
+
+      x = mod_n.multiply((x + 1), x);
+
+      d = gcd(y - x, n);
+      if(d != 1 && d != n)
+         return d;
+
+      if(i == k)
+         {
+         y = x;
+         k = 2*k;
+         }
+      }
+   return 0;
+   }
+
+// Remove (and return) any small (< 2^16) factors
+std::vector<BigInt> remove_small_factors(BigInt& n)
+   {
+   std::vector<BigInt> factors;
+
+   while(n.is_even())
+      {
+      factors.push_back(2);
+      n /= 2;
+      }
+
+   for(u32bit j = 0; j != PRIME_TABLE_SIZE; j++)
+      {
+      if(n < PRIMES[j])
+         break;
+
+      BigInt x = gcd(n, PRIMES[j]);
+
+      if(x != 1)
+         {
+         n /= x;
+
+         u32bit occurs = 0;
+         while(x != 1)
+            {
+            x /= PRIMES[j];
+            occurs++;
+            }
+
+         for(u32bit k = 0; k != occurs; k++)
+            factors.push_back(PRIMES[j]);
+         }
+      }
+
+   return factors;
+   }
+
+std::vector<BigInt> factorize(const BigInt& n_in,
+                              RandomNumberGenerator& rng)
+   {
+   BigInt n = n_in;
+   std::vector<BigInt> factors = remove_small_factors(n);
+
+   while(n != 1)
+      {
+      if(check_prime(n, rng))
+         {
+         factors.push_back(n);
+         break;
+         }
+
+      BigInt a_factor = 0;
+      while(a_factor == 0)
+         a_factor = rho(n, rng);
+
+      std::vector<BigInt> rho_factored = factorize(a_factor, rng);
+      for(u32bit j = 0; j != rho_factored.size(); j++)
+         factors.push_back(rho_factored[j]);
+
+      n /= a_factor;
+      }
+   return factors;
+   }
+
+}
+
+int main(int argc, char* argv[])
+   {
+   if(argc != 2)
+      {
+      std::cerr << "Usage: " << argv[0] << " integer\n";
+      return 1;
+      }
+
+   Botan::LibraryInitializer init;
+
+   try
+      {
+      BigInt n(argv[1]);
+
+      AutoSeeded_RNG rng;
+
+      std::vector<BigInt> factors = factorize(n, rng);
+      std::sort(factors.begin(), factors.end());
+
+      std::cout << n << ": ";
+      std::copy(factors.begin(),
+                factors.end(),
+                std::ostream_iterator<BigInt>(std::cout, " "));
+      std::cout << "\n";
+      }
+   catch(std::exception& e)
+      {
+      std::cout << e.what() << std::endl;
+      return 1;
+      }
+   return 0;
+   }